Loyola University Chicago- Course Offerings

Course Offerings

Undergraduate mathematics

Math 100. Intermediate Algebra

Prerequisite: None.

Fundamentals of algebra. Graphs of linear equations, polynomials and factoring, first and second-degree equations and inequalities, radicals and exponents, and systems of equations. Word problems emphasized throughout the course.

Math 108. Quantitative Literacy

Prerequisite: Math Placement Test or MATH 100.

An introduction to mathematical modeling. Topics chosen from linear programming, probability theory, Markov chains, scheduling problems, coding theory, social choice, voting theory, geometric concepts, game theory, graph theory, combinatorics, networks. Emphasis placed upon demonstrating the usefulness of mathematical models in other disciplines, especially the social sciences and business.

Math 117. College Algebra

Prerequisite: Math Placement Test or MATH 100.

Functions and their graphs, with emphasis on polynomials and rational functions. Complex numbers, synthetic division, binomial theorem, inverse functions, conic sections, the remainder and factor theorems, fundamental theorem of algebra. Word problems emphasized throughout the course.

Math 118. Precalculus

Prerequisite: Math Placement Test or MATH 117.

Exponential and logarithmic functions. Trigonometric functions, trigonometric identities and equations. Law of sines, law of cosines, area problems, and Heronï¿½s formula. The complex plane and DeMoivre's theorem. Vectors and parametric equations. Polar coordinates. Mathematical induction. Review of conic sections. Optimization problems. Gaussian elimination, partial fractions. Word problems emphasized throughout the course.

Math 131. Elements of Calculus I

Prerequisite: Math Placement Test or MATH 118.

An introduction to differenial and integral calculus, taught at the intuitive level, intended primarily for students in the life and social sciences, computer science, and business. Topics include: limits, continuity, differentiation, exponential growth and decay, integration, area, the fundamental theorem of calculus, chain-rule, curve-sketching including concavity, applied max/min problems.

(Students may not receive credit for both MATH 131 and 161 without permission of the departmental chair.)

Math 132. Elements of Calculus II

Prerequisite: MATH 131.

A continuation of MATH 131. Topics include: properties of the integral, techniques of integration, numerical methods, improper integrals, applications to geometry, physics, economics, and probability theory, introduction to differential equations and mathematical modeling, systems of differential equations, and the Taylor series.

Math 161. Calculus I (4 credit hours)

Prerequisite: Math Placement Test or Math 118.

A traditional introduction to differential and integral calculus. Functions, limits, continuity, differentiation, intermediate and mean-value theorems, curve sketching, optimization problems, related rates, definite and indefinite integrals, fundamental theorem of calculus, log and exponential functions. Applications to physics and other disciplines.

(Students may not receive credit for both MATH 161 and MATH 131 without permission of the departmental chair.)

Math 162. Calculus II (4 credit hours)

Prerequisite: MATH 161.

A continuation of MATH 161. Calculus of logarithmic, exponential, inverse trigonometric, and hyperbolic functions. Techniques of integration. Applications of integration to volume, surface area, arc length, center of mass, and work. Numerical sequences and series. Study of power series and the theory of convergence. Taylor's theorem with remainder.

Math 201. Elementary Number Theory

Prerequisite: Math 118

This course serves primarily as an introduction to understanding and constructing proofs for students planning to take advanced 300-level courses in mathematics. Topics include: mathematical induction, the Euclidean algorithm, congruences, Wilson's theorem, Fermat's little theorem, Euler's phi function, prime numbers, Mersenne primes, and quadratic reciprocity. As time permits, additional topics may include: applications to cryptography, Pell's equation, diophantine approximation, primality testing, Carmichael numbers, Gaussian integers, continued fractions, algebraic numbers, and transcendental numbers.

Math 212. Linear Algebra

Prerequisite: MATH 162 or 132.

An introduction to linear algebra in abstract vector spaces with particular emphasis on R^n. Topics include: Gaussian elimination, matrix algebra, linear independence, span, basis, linear transformations, determinants, eigenvalues, eigenvectors, and diagonalization. Some of the basic theorems will be proved rigorously; other results will be demonstrated informally. Software such as MAPLE may be utilized.

Math 215. Object Oriented Math Programming

Prerequisite: MATH 162.

This is an introductory programming course for students interested in mathematics and scientific computing. Students will program primarily in a general object-oriented language such as Python, with supplementary exercises in a computer algebra system. Examples will be drawn primarily from applications of calculus, elementary number theory, and cryptography.

Math 263. Multivariable Calculus (5 hours)

Prerequisite: MATH 162 preferred but Math 132 is acceptable.

Vectors and vector algebra, vector-valued functions, functions of several variables, differential and integral calculus of functions of several variables, and advanced topics including change of variables in multiple integration, Green's Theorem, the Divergence Theorem, and Stokes' Theorem. Software such as MAPLE may be utilized.

Math 264. Ordinary Differential Equations

Prerequisite: MATH 263.

Techniques for solving linear and non-linear first and second-order differential equations, the theory of linear second-order equations with constant coefficients, power series solutions of second-order equation, and topics in systems of linear first-order differential equations. Software such as MAPLE may be utilized.

Math 277. Problem Solving Seminar (1-2 credit hours)

Prerequisite: Math 162.

In a seminar setting, students discuss and present proofs (or computer examples) as solutions to regional and national mathematics contest problems usually involving techniques drawn from elementary logic, calculus of one and several variables, combinatorics, number theory, geometry, basic algebra, and abstract algebra.

Math 298. Mathematics Seminar (1-3 credit hours)

Prerequisite: MATH 162.

A sophomore-level seminar which may cover topics in number theory, logic, set theory, metric spaces, or history of mathematics.

Math 301. History of Mathematics

Prerequisite: MATH 132 or 162. MATH 201 is recommended.

This course explores selected topics in the history of mathematics ranging from Babylonian and Egyptian mathematics to Pythagoras and Euclid to the Hindu-Arabic numeration system to Newton and Leibniz to geometries other that Euclid's to the mathematical art of Escher.

Math/Stat 304. Probability & Statistics I

Prerequisites: MATH 263; STAT 203 or 335.

A calculus-based introduction to probability theory. Combinatorial analysis, random walks, conditional probability and stochastic independence, the binomial, Poisson and exponential distributions, the normal approximation to the binomial distribution, random variables, expectation, laws of large numbers, moment generating functions and Markov chains.

Math/Stat 305. Probability & Statistics II

Prerequisite: STAT 304.

A continuation of STAT 304. Hypothesis testing, limit theorems, point and interval estimation, linear correlation, and linear regression.

Math/Stat 306. Stochastic Processes

Prerequisites: STAT 203 or 335; MATH 212.

Finite-state Markov processes. Markov chains, classification of states, long-run behavior, continuous time processes such as the Poisson process, birth and death processes, random walks, and Brownian motion. Examples in genetics, population growth, inventory, cash management, and the gambling theory.

Math 309. Numerical Methods

Prerequisites: Math 215 or COMP 270; MATH 212, 264.

Introduction to error analysis, numerical solution of equations, interpolation and approximation, numerical differentiation and integration, matrices and solution of systems of equations, numerical solution of ordinary and partial differential equations.

Math 313. Abstract Algebra

Prerequisite: MATH 201 and 212.

A rigorous introduction to the study of abstract algebraic systems with emphasis on the theory of groups. Equivalence relations, subgroups, homomorphisms, quotients, products, linear groups, permutation groups, and selected advanced topics.

Math 314. Advanced Topics in Abstract Algebra.

Prerequisite: MATH 313.

Study of commutative and non-commutative rings, integral domains, and fields. Selected topics may include Galois theory, group representations, modules, and advanced group theory.

Math 315. Advanced Topics in Linear Algebra

Prerequisite: MATH 313.

An abstract approach to the study of vector spaces and transformations. Selected topics may include similarity, duality, canonical forms, inner products, bilinear forms, Hermitian and unitary spaces.

Math 318. Combinatorics

Prerequisite: MATH 162.

Induction, pigeon-hole principle, permutations, combinations, recurrence relations, generating functions, and inclusion-exclusion principle. Topics drawn from partitions, graph theory, graph coloring, and combinatorial design, Polya's theory, Ramsey's theorem, and optimization problems.

Math 320. Mathematical Logic

Prerequisite: MATH 313.

This course in modern mathematical logic begins with a study of propositional logic and leads to an examination of first-order predicate logic including quantifiers, models, syntax, semantics, and the completeness and compactness theorems. Additional topics include Goedel's incompleteness theorems. Connections with abstract algebra and other areas of mathematics are explored.

Math 328. ALGEBRAIC CODING THEORY

Codes with algebraic structure for error control are examined. Block codes including Hamming codes and Reed-Muller codes, BCH codes, and other cyclic codes and their implementation are treated. Other topics may include: convolutional codes, effciency considerations, and Shannon's fundamental theorem of information theory.

Math 331. Cryptography (COMP 331)

Prerequisite: COMP 363 or MATH 313 or 201.

This course introduces the formal foundations of cryptography and also investigates some well-known standards and protocols, including private and public key cryptosystems, hashing, digital signatures, RSA, DSS, PGP, and related topics

Math 344. Geometry

Prerequisite: MATH 132 or 162. MATH 201 is recommended.

Axiomatic systems which define geometries. Topics in Euclidean and non-Euclidean geometry.

Math 351. Introduction to Real Analysis I

Prerequisites: MATH 201, 212.

A rigorous treatment of properties and applications of real numbers and real-valued functions of a real variable. Topics include: sequences, limits, the Bolzano-Weierstrass theorem, compactness and the Heine-Borel theorem, connectedness, topology, continuity, uniform continuity, fixed-point theorem, derivatives.

Math 352. Introduction to Real Analysis II

Prerequisite: MATH 351.

Continuation of Math 351. Differentiability and integrability on R^1 and R^m. Topics such as Taylor's theorem, the change of variable theorem, the inverse and implicit function theorems, and Lebesgue integration.

Math 353. Introductory Complex Analysis

Prerequisites: MATH 264, 351.

An introduction to the theory of functions of a complex variable. Topics include analytic functions, contour integrals, Cauchy integral formula, harmonic functions, Liouville's theorem, Laurent series, residues and poles, and conformal mapping. Additional topics may include the Picard theorems, Rouche's theorem, Schwarz-Christoffel transformations, and Riemann surfaces.

Math 355. Methods of Applied Mathematics

Prerequisite: MATH 264.

A wide spectrum of topics with applications to physics, engineering, economics, and the social sciences. Topics include Green's functions and solutions to ordinary differential equations, integral equations, the calculus of variations and optimization, and partial differential equations.

Math 358. Methods in Operations Research (STAT 358)

Prerequisites: MATH 212 and STAT 203 or 335.

An introduction to linear programming, integer and non-linear programming, queuing theory, and game theory. Emphasis will be placed upon mathematical modeling of problems in economics, business, finance, and the behavioral sciences.

Math 360. Introduction to Game Theory

Prerequisites: Stat 203 and Math 212.

The noncooperative and cooperative theories of games. Two person zero sum matrix games, nonzero sum N-person games, Nash equilibria of games with a continuum of strategies, auctions, duels. Cooperative game theory, including the theory of bargaining, the theory of fair allocation of rewards using the nucleolus and using the Shapley value.

Math 386. Introduction to Topology

Prerequisite: MATH 351.

Topological spaces, continuity, connectedness, path-connectedness, compactness, product spaces, Tychonoff's theorem, and the Baire category theorem. Additional topics may include space-filling curves, quotient spaces, topological dimension, Hausdorff dimension, homotopy theory, and filters.

Math 388. Special Topics in Mathematics (1-3 credit hours)

Advanced topics in mathematics, including analysis, topology, algebra, applied mathematics, and logic. Course title and content vary; prerequisites are established by the instructor. May be repeated for credit.

Math 398. Independent Study (1-3 credit hours)

Prerequisite: permission of chair.

Independent study of selected topics in mathematics under the supervision of a faculty member. May be repeated for credit.

Math 399H. Honors Tutorial (1-3 credit hours)

Prerequisite: permission of chair.

Independent study of selected topics in mathematics for students in the honors program. May be repeated for credit.

Undergraduate Statistics

Stat 103. Fundamentals of Statistics

Prerequisite: Math Placement Test or MATH 100 (with a grade of "C" or better).

An introduction to statistical reasoning. Students learn how statistics has helped to solve major problems in economics, education, genetics, medicine, physics, political science, and psychology. Topics include: design of experiments, descriptive statistics, mean and standard deviation, the normal distribution, the binomial distribution, correlation and regression, sampling, estimation, and testing of hypothesis.

Stat 203. Statistics

Prerequisite: Math 162 or 132 (with grade of "C" or better).

An introduction to statistical methodology and theory using the techniques of one-variable calculus. Topics include: experimental design, descriptive statistics, probability theory, sampling theory, inferential statistics, estimation theory, testing hypotheses, correlation theory, and regression.

(Note: Students may not receive credit for both STAT 203 & 335.)

Stat 303. SAS Programming and Applied Statistics

Prerequisite: STAT 103 or 203 or 335.

An introduction to SAS programming in the context of practical problems taken from applied statistics. SAS programming includes extensive data-set manipulations such as inputting, from raw data and external files, subsetting, working with single and multidimensional arrays, SAS functions, basic macros. SAS procedures include MEANS, FREQ, GLM, PLOT, REG, UNIVARIATE, and selected topics from IML, LOGISTIC, MIXED, NLIN. Statistical topics include t-tests, simple and multiple regression, ANOVA, categorial analysis, repeated measures.

Stat 304. Probability & Statistics I (MATH 304)

Prerequisites: MATH 263; STAT 203 or 335.

Stat 305. Probability & Statistics II (MATH 305)

Prerequisite: STAT 304.

A continuation of STAT 304. Hypothesis testing, limit theorems, point and interval estimation, linear correlation, and linear regression.

Stat 306. Stochastic Processes (MATH 306)

Prerequisites: STAT 203 or 335; MATH 212.

Stat 307. Statistical Design and Analysis of Experiments

Prerequisites: STAT 203 or 335.

Comparative experiments, analysis of variance, fixed and random effects models, randomized block designs, Latin square designs, incomplete block designs, and factorial designs. Use of packaged computer programs such as SPSS or SAS.

Stat 308. Applied Regression Analysis

Prerequisites: STAT 203 or 335.

Simple and multiple linear regression methods including weighted least squares and polynomial regression. Multiple comparison estimation procedures, residual analysis, and other methods for studying the aptness of a proposed regression model. Use of packaged computer programs such as SPSS and SAS.

Stat 310. Categorical Data Analysis

Prerequisite: STAT 203 or STAT 335

An introduction to modern-day extensions of simple linear regression and ANOVA to the chi-square test including logistic regression and log-linear modelling techniques based on generalized linear models. Methods for matched-pair, small datasets, ordinal and multi-category data are also discussed. This course focuses on applications using real-life data sets, and uses popular software packages.

Stat 335. Introduction to Biostatistics (BIOL 335) (4 credit hours)

Prerequisites: MATH 162 or 132; BIOL 102.

An introduction to statistical methods used in designing biological experiments and in data analysis. Topics include probability and sampling distribution, design of biological experiments and analysis of variance, regression and correlation, stochastic processes, and frequency distributions. Computer laboratory assignments with biological data.

(Note: Students may not receive credit for both STAT 203 & 335.)

Stat 336. Advanced Biostatistics

Prerequisites: STAT 335.

An intensive study of experimental design (including interaction, analysis of covariance, and crossover designs) and the analysis of designed studies, simple and multiple linear regression, generalized linear and nonlinear regression (logistic and log-linear models), bioassay, relative potency and drug synergy, multivariate analysis (including MANOVA and multivariate regression), repeated measures (designs and analysis), and survival analysis (Cox proportional odds, log-rank tests, Kaplan-Meier estimation) of censored data. The emphasis is on applications instead of statistical theory, and students are required to analyze real-life datasets using statistical packages such as Minitab and SAS, though no previous programming experience is assumed.

Stat 337. Quantitative Methods in Bioinformatics

Prerequisite: STAT 203 or 335 or equivalent.

This course explores recently developed mathematical, probabilistic and statistical methods currently used in the fields of bioinformatics and DNA microarray and protein array data analysis. These include stochastic processes, (hidden and traditional) Markov chains, tree- and clustering techniques (including principal components analysis and biplots), discriminant analysis, experimental design strategies and ANOVA methods. Our focus in this course is on the application of these techniques and on meaningful interpretation of results.

Stat 356. Computer Principles of Modeling and Simulation (COMP 356)

Prerequisites: Math 215 or COMP 170 or 125; STAT 203 or 335.

Random number generators, random variable generators, principles of modeling, Monte Carlo methods, and introduction to simulation languages such as QSIM, AWESIM or ARENA. Applications to management sciences and decision-making.

Stat 358. Methods in Operations Research (math 358)

Prerequisites: MATH 212 and STAT 203 or 335.

Stat 388. Special Topics in Statistics (1-3 credit hours)

Prerequisite: STAT 303.

Advanced topics in statistics, such as multivariate analysis, sampling theory, non-parametric methods, decision theory, and Bayesian analysis.

Course title and content vary; prerequisites are established by the instructor. May be repeated for credit.

Stat 396. Actuarial Seminar I (1 credit hour)

Prerequisites: Math 263, Math 212, Stat 304 are strongly recommended.

Description: This seminar is for students who want to prepare for Society of Actuaries exam P, or (CAS Exam 1), Probability. Topics include general probability including conditional probability and Bayes rule, univariate distributions, including binomial, hypergeometric, Poisson, beta, Pareto, gamma, Weibull and normal, and multivariate distributions including joint moment generating functions and transformation techniques.

May be repeated for credit.

Stat 397. Actuarial Seminar II (1 credit hour)

Prerequisite: STAT 304.

Description: The first actuarial exam (Examination 101) covers material from multivariate calculus and probability, and whereas STAT 396 reviews differential, integral and multivariate calculus, this course reviews probability theory. This seminar is highly recommended for students considering a career in the actuarial field.

May be repeated for credit.

Stat 398. Independent Study (1-3 credit hours)

Prerequisite: permission of chair.

Independent study of selected topics in statistics under the supervision of a faculty member.

May be repeated for credit.

Stat 399H. Honors Tutorial (1-3 credit hours)

Prerequisite: permission of chair.

Independent study of selected topics in statistics for students in the honors program.

May be repeated for credit.

Graduate Mathematics

Stat 404/405. Probability and Statistics (Stat 404/405)

Prerequisite: STAT 203/304.

Probability spaces, continuous and discrete random variables and distributions, moment generating functions, law of large numbers, central limit theorem, hypothesis testing, point and interval estimates, regression analysis.

Math 409 (Comp 409). Advanced Numerical Analysis

Prerequisites: MATH 212, 264; COMP 271.

Computational methods, convergence and stability, error analysis of solutions to differential equations, matrix inversion and calculation of eigenvalues and eigenvectors are examined.

Math 413/414. Algebra I & II

Prerequisites: MATH 313, 314.

A standard graduate sequence in algebra. Covers basic algebraic structures: groups, rings, fields, integral domains, vector spaces, modules, etc., Additional topics chosen from the following: Galois theory, linear groups, Dedekind domains, category theory, tensor products, homological algebra, and representation theory.

Math 421. Mathematical Modeling and Computer Simulation (COMP 421)

Prerequisites: MATH 215 or COMP 125 or 170; MATH 132 or 162; STAT 203.

This course covers the theory and design of modeling applicable to the physical, social, life, and management sciences. Models involving Markov chains, optimization, graph theory, networks, growth processes, queuing theory, and differential equations are examined. A computer simulation language such as SLAM, SIMSCRIPT, or AWESIM is utilized to model complex phenomena. Random number generators are studied in depth.

Math 423. Combinatorial Mathematics (COMP 423)

Prerequisite: MATH 313 or COMP 211.

This course presents generation and enumeration of configurations, recurrence relations, generating functions, Polya's theorem, combinatorial design, graph theory, combinatorial algorithms and computer applications.

Math 428. Algebraic Coding Theory (COMP 428)

Prerequisite: MATH 212; COMP 211 or MATH 313.

Codes with algebraic structure for error control are examined. Block codes including Hamming codes and Reed-Muller codes, BCH codes, quadratic residue codes, and other cyclic codes and their implementation are treated. Other topics may include: convolutional codes, efficiency considerations, and Shannon's fundamental theorem of information theory.

Math 431. Cryptography (See COMP 431)

Math 441. General Topology

General theory of topological and metric spaces, compact spaces, convergence and completeness in metric spaces, connected spaces.

Math 445. Financial Mathematics I

Prerequisites: STAT 203, MATH 264, MATH 212.

Options Markets, Black-Scholes Pricing Formulas, Stochastic Calculus, Hedging Schemes, Binomial Option Pricing, Exotic Options, General Derivaties.

Math 446. Financial Mathematics II

Prerequisites: STAT 203, MATH 264, COMP 125 or 170, MATH 212.

Securities Models, Optimal Portfolios, Equilibrium Models, Optimal Consumption and Investment, Arbitrage Pricing, Advanced Contingent Claims.

Math 451. Analysis I

Prerequisites: MATH 351.

Foundation of analysis; measure theory, Lebesgue integration; Hilbert and Banach spaces, complex analysis.

Math 452. Analysis II

Prerequisite: MATH 451.

Fubini Theorem; differentiation; linear and nonlinear functional analysis.

Math 455. Applied Mathematics

Prerequisite: Math 264.

Introduction to modern applied math; calculus of variations, partial differential equations, techniques for solutions of partial differential equations.

Math 476. Automata and Formal Languages (See COMP 476)

Math 478. Topics in Operations Research (COMP 478)

Prerequisites: MATH 162, 212; STAT 303.

This course presents the study of selected mathematical models and their application to applied problems. Topics in linear and mathematical programming, optimization theory, and game theory are examined.

Math 488. Topics in Mathematics and Statistics

Prerequisite: minimum of two graduate core courses.

This course treats selected topics not normally covered in the department's regular offerings. This course may be repeated for credit.

Math 499. Independent Study

Prerequisite: permission of the graduate director.

This is a directed study course undertaken by advanced students and supervised by a member of the graduate faculty.

Math 605. Master of Science Study

Prerequisite: completion of the graduate core courses.

This course is a non-credit means of permitting students to be formally enrolled at Loyola while preparing for the written comprehensive examination.